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1996 | 69 | 2 | 167-178
Tytuł artykułu

The unconditional pointwise convergence of orthogonal seriesin $L_2$ over a von Neumann algebra

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper is devoted to some problems concerning a convergence of pointwise type in the $L_2$-space over a von Neumann algebra M with a faithful normal state Φ [3]. Here $L_2 = L_2(M,Φ)$ is the completion of M under the norm $x → |x|^2 = Φ(x*x)^{1/2}$.
Słowa kluczowe
Rocznik
Tom
69
Numer
2
Strony
167-178
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-07-29
Twórcy
autor
  • Institute of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland
  • Institute of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland
  • Institute of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] G. Alexits, Convergence Problems of Orthogonal Series, Pergamon Press, New York, 1961.
  • [2] C. J. K. Batty, The strong law of large numbers for states and traces of a W*-algebra, Z. Wahrsch. Verw. Gebiete 48 (1979), 177-191.
  • [3] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics I, Springer, New York, 1979.
  • [4] M. S. Goldstein, Theorems in almost everywhere convergence, J. Operator Theory 6 (1981), 233-311 (in Russian).
  • [5] E. Hensz, Strong laws of large numbers for orthogonal sequences in von Neumann algebras, in: Proc. Probability Theory on Vector Spaces IV, Łańcut 1987, Lecture Notes in Math. 1391, Springer, 1989, 112-124.
  • [6] E. Hensz and R. Jajte, Pointwise convergence theorems in $L_2$ over a von Neumann algebra, Math. Z. 193 (1986), 413-429.
  • [7] E. Hensz, R. Jajte and A. Paszkiewicz, Topics in pointwise convergence in $L_2$ over a von Neumann algebra, Quantum Probab. Related Topics 9 (1994), 239-271.
  • [8] R. Jajte, Strong limit theorems for orthogonal sequences in von Neumann algebras, Proc. Amer. Math. Soc. 94 (1985), 229-236.
  • [9] R. Jajte, Strong Limit Theorems in Noncommutative Probability, Lecture Notes in Math. 1110, Springer, Berlin, 1985.
  • [10] R. Jajte, Almost sure convergence of iterates of contractions in noncommutative $L_2$-spaces, Math. Z. 205 (1990), 165-176.
  • [11] R. Jajte, Strong Limit Theorems in Noncommutative $L_2$-Spaces, Lecture Notes in Math. 1477, Springer, Berlin, 1991.
  • [12] E. C. Lance, Ergodic theorem for convex sets and operator algebras, Invent. Math. 37 (1976), 201-214.
  • [13] W. Orlicz, Zur Theorie der Orthogonalreihen, Bull. Internat. Acad. Polon. Sci. Sér. A (1927), 81-115.
  • [14] A. Paszkiewicz, Convergence in W*-algebras, J. Funct. Anal. 69 (1986), 143-154.
  • [15] I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. 57 (1953), 401-457.
  • [16] Ya. G. Sinai and V. V. Anshelevich, Some problems of non-commutative ergodic theory, Russian Math. Surveys 31 (1976), 157-174.
  • [17] K. Tandori, Über die orthogonalen Funktionen X (unbedingte Konvergenz), Acta Sci. Math. (Szeged) 23 (1962), 185-221.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv69i2p167bwm
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